Ex 12.3, 7
In figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
Since square has all angles 90
Area of shaded region
= Area of square ABCD
Area of 4 quadrants of circles
Area of square ABCD
Given side of square = 14 cm
Area of the square = (Side)2
= (14)2
= (14 14)
= 196 cm2
Area of 4 quadrants of circles
In the question, diagram shows symmetry
radius of the circle would be equal.
In every single diagrams radius = ( )/2
= 14/2 = 7
So, radius = r = 7 cm
Now ,
Area of one quadrant = 1/4 Area of circle
= 1/4 2
= 1/4 22/7 (72)
= 1/4 22 (7 7)
= 1/4 22 49
= 154/4 cm2
Area of 4 quadrants = 4 area of quadrant
= 4 154/4
= 154 cm2
Area of shaded region = Area of square - Area of 4 quadrant
= 196 154
= 42 cm2
Hence, area of shaded region = 42 cm2